NCERT Solutions Class 8 Maths Chapter 7 Comparing Quantities

NCERT Solutions for Class 8 Maths Comparing Quantities provide step-by-step explanations for ratios, percentages, increase and decrease in percentage, profit and loss, discount, tax, and simple and compound interest. These solutions help students understand the formulas and methods used to solve questions from the chapter.

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Comparing Quantities Class 8 Questions and Answers

Comparing quantities means finding the relationship between two quantities. In this chapter, students use ratios and percentages to compare values and solve problems related to prices, profit, loss and interest.

The major concepts covered include:

• Ratio and percentage

• Converting fractions and decimals into percentages

• Converting percentages into fractions or decimals

• Increase or decrease as a percentage

• Buying and selling

• Cost price and selling price

• Profit and loss

• Discount

• Simple interest

• Compound interest

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Comparing Quantities Class 8 NCERT Solutions

The NCERT chapter is divided into three exercises covering percentage and comparison, buying and selling, and interest. The exercise-wise solutions help students identify the correct formula before solving a question.

Exercise 8.1: Ratio and Percentage

The first exercise focuses on comparing quantities using ratios and percentages.

Important question types include:

• Finding ratios between quantities
• Converting ratios into percentages
• Finding a percentage of a quantity
• Finding the original quantity when a percentage is known
• Finding the remaining percentage
• Solving percentage-based word problems

Students can explore more Class 8 maths concepts, percentage topics, and age-appropriate learning resources on Curious Jr.

Example: Converting a ratio into percentage

Suppose the ratio is 3:4.

Convert it into a fraction:

3/4

Now multiply by 100:

(3/4) × 100 = 75%

Therefore, 3:4 = 75%.

Example: Finding a percentage

Find 25% of ₹800.

25% of ₹800 = (25/100) × 800

= ₹200

Therefore, 25% of ₹800 is ₹200.

Exercise 8.2: Increase, Decrease, Profit, Loss and Discount

This exercise includes questions based on changes in price, buying and selling, profit, loss and discount.

Important terms include:

Cost Price (CP): The price at which an item is purchased.

Selling Price (SP): The price at which an item is sold.

Profit: When the selling price is greater than the cost price.

Loss: When the selling price is less than the cost price.

Discount: The reduction offered on the marked price of an item.

Profit and Loss Formulas

Profit = SP − CP

Loss = CP − SP

Profit % = (Profit/CP) × 100

Loss % = (Loss/CP) × 100

Discount Formula

Discount = Marked Price − Selling Price

Discount % = (Discount/Marked Price) × 100

Example: Profit Percentage

If an article is bought for ₹500 and sold for ₹600:

Profit = ₹600 − ₹500 = ₹100

Profit % = (100/500) × 100

= 20%

Therefore, the profit is 20%.

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Exercise 8.3: Simple and Compound Interest

The third exercise deals with simple interest and compound interest, including questions involving different time periods and rates of interest.

Simple Interest Formula

SI = (P × R × T)/100

where:

• P = Principal

• R = Rate of interest per year

• T = Time in years

Compound Interest

For annual compounding:

A = P(1 + R/100)ⁿ

where:

• A = Amount

• P = Principal

• R = Rate of interest

• n = Number of years

Compound Interest = Amount − Principal

Comparing Quantities Class 8 Extra Questions and Answers

After completing the NCERT exercises, students can practise extra questions based on the same concepts.

1. Find 15% of 600.

Solution:

15% of 600 = (15/100) × 600

= 90

2. Convert 2:5 into a percentage.

Solution:

2/5 × 100 = 40%

3. An article costs ₹800 and is sold for ₹920. Find the profit and profit percentage.

Solution:

Profit = ₹920 − ₹800 = ₹120

Profit % = (120/800) × 100

= 15%

Therefore, the profit is ₹120 or 15%.

4. A shirt marked at ₹1,500 is sold for ₹1,200. Find the discount.

Solution:

Discount = ₹1,500 − ₹1,200

= ₹300

Discount % = (300/1500) × 100

= 20%

5. Find the simple interest on ₹5,000 at 8% per annum for 2 years.

Solution:

SI = (P × R × T)/100

= (5000 × 8 × 2)/100

= ₹800

6. What is the difference between simple interest and compound interest?

Answer: Simple interest is calculated on the original principal, while compound interest is calculated on the principal along with the accumulated interest.

Comparing Quantities Class 8 Important Formulas

Comparing Quantities Class 8 Questions: Common Mistakes

While solving Comparing Quantities Class 8 questions, check the following:

• Use the original value when calculating percentage increase or decrease.

• Use cost price as the base when calculating profit or loss percentage.

• Do not confuse marked price with selling price when calculating discount.

• Convert time into the required unit before using the interest formula.

• Write the percentage sign when the answer is expressed as a percentage.

• Check whether the question asks for the interest or the total amount.

Comparing Quantities Class 8 Extra Questions for Practice

Try these questions before checking the solution:

1. Find 35% of 480.

2. Convert 3:5 into a percentage.

3. An article bought for ₹900 is sold for ₹1,080. Find the profit percentage.

4. A marked price of ₹2,000 is reduced to ₹1,700. Find the discount percentage.

5. Find the simple interest on ₹4,000 at 5% per annum for 3 years.

6. Find the amount when ₹6,000 is invested at 10% compound interest annually for 2 years.

These questions cover the major concepts students encounter while practising Comparing Quantities Class 8 extra questions.

Comparing Quantities Class 8: Quick Revision

Before solving a question, identify what it is asking:

Ratio → Compare two quantities.

Percentage → Express a quantity out of 100.

Increase/Decrease → Compare the change with the original value.

Profit/Loss → Compare selling price with cost price.

Discount → Compare the marked price with the reduced selling price.

Simple Interest → Calculate interest on the principal.

Compound Interest → Calculate interest on the principal plus accumulated interest.

This approach helps students select the correct formula instead of trying to memorise every question separately.